While it is unethical academic practice to "provide" an analysis for you, I am happy to help guide toward developing your own. The first step is to clarify what a rhetorical analysis is. The second step is to clarify components to analyze. A rhetorical analysis is an examination of an argument someone makes. You determine the method and techniques of how the argument is made. You are not interested in truth ("Is this argument true?") you are interested in how the argument is made and whether it is successfully made.

Let's look at Viola's soliloquy in light of a few of these particulars.

I left no ring with her. What means this lady?Fortune forbid my outside have not charmed her!

These opening lines indicate that this is a complex rhetorical speech. (1) She is trying to answer a question. (2) She is trying to make sense of her experience. (3) She seems to be trying to persuade herself of the nature of her experience. The last lines show us her conclusion, which is important in knowing if her rhetorical method and technique succeeded:

O time, thou must untangle this, not I.It is too hard a knot for me to untie!

Since Viola makes proofs with no external data, no opinion polls, no surveys or statistical analyses, we define her method as an artistic proof from within her own thoughts. She assumes she believes herself and considers her thoughts valid. One external proof appears at the end, but it is a metaphorical proof through personified Time, thus invalid as an inartistic proof.

What kind of appeal, pathetic, ethical, or logical, does she make? While Viola clearly feels emotional and confused, she is appealing to logic as these two lines show:

I am the man. If it be so, as ’tis,Poor lady, she were better love a dream.

Olivia has called Viola "the man," as in the man for me. Viola sorts this out by examining it with a logical "if/then" conditional: if something, [then] something else. Viola's logical conclusion is that Olivia would do better to "love a dream" than to love Viola disguised as a man!

A technique used is amplification. Viola elaborates upon this confounding situation adding ideas to amplify the effects to arrest our attention as we advance through her thoughts.

She made good view of me, indeed so muchThat sure methought her eyes had lost her tongue,For she did speak in starts distractedly.She loves me, sure! / [...] / love a dream.

Im sorry but I see that a full answer has been given for this student, which is not quite done I believe. How are students ever going to get to study if they are going to be spoonfed in this manner? I joined this site because it had a good reputation for helping and guiding students at various levels, without overtly answering or helping cheat, and encouraging self-work, finally. But I feel rather disappointed to see this. I hope both question and answer are removed or redirected to some appropriate place, maybe in Notes section for reference? Thank you.